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Prioritized conditional imperatives: problems and a new proposal

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Abstract

The sentences of deontic logic may be understood as describing what an agent ought to do when faced with a given set of norms. If these norms come into conflict, the best the agent can be expected to do is to follow a maximal subset of the norms. Intuitively, a priority ordering of the norms can be helpful in determining the relevant sets and resolve conflicts, but a formal resolution mechanism has been difficult to provide. In particular, reasoning about prioritized conditional imperatives is overshadowed by problems such as the ‘order puzzle’ that are not satisfactorily resolved by existing approaches. The paper provides a new proposal as to how these problems may be overcome.

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References

  1. Alchourrón, C. E., & Bulygin, E. (1981). The expressive conception of norms. In [18], 95–124.

  2. Alchourrón, C. E., & Makinson, D. (1981). Hierarchies of regulations and their logic. In R. Hilpinen (Ed.), New Studies in Deontic Logic (pp. 125–148). Dordrecht: Reidel.

    Google Scholar 

  3. Brewka, G. (1989). Preferred subtheories: An extended logical framework for default reasoning. In N. S. Sridharan (Ed.), Proceedings of the eleventh international joint conference on artificial intelligence IJCAI-89, Detroit, Michigan, USA, August 20–25, 1989 (pp. 1043–1048). San Mateo, Calif.: Kaufmann.

  4. Brewka, G. (1994). Reasoning about priorities in default logic. In B. Hayes-Roth & R. E. Korf (Eds.), Proceedings of the 12th national conference on artificial intelligence, Seattle, WA, July 31st–August 4th, 1994 (Vol. 2 pp. 940–945). Menlo Park: AAAI Press.

  5. Brewka G., Eiter T. (1999). Preferred answer sets for extended logic programs. Artificial Intelligence 109, 297–356

    Article  MATH  MathSciNet  Google Scholar 

  6. Broersen J., Dastani M., van der Torre L. (2002). Realistic desires. Journal of Applied Non-Classical Logics 12, 287–308

    Article  MATH  MathSciNet  Google Scholar 

  7. Caminada, M., & Sakama, C. (2006). On the existence of answer sets in normal extended logic programs. In G. Brewka, S. Coradeschi, A. Perini, & P. Traverso (Eds.), Proceedings of the 17th European conference on artificial intelligence (ECAI 2006), August 29–September 1, 2006, Riva del Garda, Italy (pp. 741–742). Amsterdam: IOS Press.

  8. Downing P. (1959). Opposite conditionals and deontic logic. Mind 63, 491–502

    Google Scholar 

  9. van Fraassen B. (1973). Values and the heart’s command. Journal of Philosophy 70, 5–19

    Article  Google Scholar 

  10. Goble L. (2005). A logic for deontic dilemmas. Journal of Applied Logic 3, 461–483

    Article  MATH  MathSciNet  Google Scholar 

  11. Greenspan P. (1975). Conditional oughts and hypothetical imperatives. Journal of Philosophy 72, 259–276

    Article  Google Scholar 

  12. Hansen J. (2004). Problems and results for logics about imperatives. Journal of Applied Logic 2, 39–61

    Article  MATH  MathSciNet  Google Scholar 

  13. Hansen J. (2005). Conflicting imperatives and dyadic deontic logic. Journal of Applied Logic 3, 484–511

    Article  MATH  MathSciNet  Google Scholar 

  14. Hansen J. (2006). Deontic logics for prioritized imperatives. Artificial Intelligence and Law 14, 1–34

    Article  Google Scholar 

  15. Hansson, B. (1969). An analysis of some deontic logics. Nôus, 3, 373–398. Reprinted in [17], 121–147.

  16. Hansson S.O. (2001). The structure of values and norms. Cambridge, Cambridge University Press

    MATH  Google Scholar 

  17. Hilpinen, R. (Ed.) (1971). Deontic logic: Introductory and systematic readings. Dordrecht, Reidel

  18. Hilpinen, R. (Ed.) (1981). New studies in deontic logic. Dordrecht, Reidel

  19. Hofstadter A., McKinsey J.C.C. (1938). On the logic of imperatives. Philosophy of Science 6, 446–457

    Article  Google Scholar 

  20. Horty J.F. (2003). Reasoning with moral conflicts. Noûs 37, 557–605

    MathSciNet  Google Scholar 

  21. Horty J.F. (2007). Defaults with priorities. Journal of Philosophical Logic 36, 367–413

    Article  MATH  MathSciNet  Google Scholar 

  22. Kraus S., Lehmann D., Magidor M. (1990). Nonmonotonic reasoning, preferential models and cumulative logics. Artificial Intelligence 44, 167–207

    Article  MathSciNet  MATH  Google Scholar 

  23. Lewis D. (1974). Semantic analysis for dyadic deontic logics. In: Stenlund S., (eds). Logical theory and semantic analysis. Reidel, Dordrecht, pp. 1–14

    Google Scholar 

  24. Makinson, D. (1999). On a fundamental problem of deontic logic. In P. McNamara & H. Prakken (Eds.), Norms, logics and information systems (pp. 29–53). Amsterdam: IOS.

  25. Makinson D., van der Torre L. (2000). Input/output logics. Journal of Philosophical Logic 29, 383–408

    Article  MATH  MathSciNet  Google Scholar 

  26. Makinson D., van der Torre L. (2001). Constraints for Input/output logics. Journal of Philosophical Logic 30, 155–185

    Article  MATH  MathSciNet  Google Scholar 

  27. Marek V.W., Truszczyński M. (1993). Nonmonotonic logic context-dependent reasoning. Berlin, Springer

    MATH  Google Scholar 

  28. Nebel, B. (1991). Belief revision and default reasoning: Syntax-based approaches. In J. A. Allen, R. Fikes & E. Sandewall (Eds.), Principles of knowledge representation and reasoning: Proceedings of the second international conference, KR ’91, Cambridge, MA, April 1991 (pp. 417–428). San Mateo: Morgan Kaufmann.

  29. Nebel B. (1992). Syntax-based approaches to belief revision. In: Gärdenfors P., (eds). Belief revision. Cambridge University Press, Cambridge, pp. 52–88

    Google Scholar 

  30. Prakken H. (1997). Logical tools for modelling legal argument. Dordrecht, Kluwer

    Google Scholar 

  31. Prakken H., Sartor G. (1997). Argument-based logic programming with defeasible priorities. Journal of Applied Non-classical Logics 7, 25–75

    MATH  MathSciNet  Google Scholar 

  32. Rescher N. (1964). Hypothetical reasoning. Amsterdam, North-Holland

    Google Scholar 

  33. Rescher N. (1966). The Logic of commands. London, Routledge & Kegan Paul

    Google Scholar 

  34. Rintanen, J. (1994). Prioritized autoepistemic logic. In: C. MacNish, D. Pearce, & L. M. Pereira (Eds.), Logics in artificial intelligence, European Workshop, JELIA ’94, York, September 1994, Proceedings (pp. 232–246). Berlin: Springer.

    Google Scholar 

  35. Ross W.D. (1930). The right and the good. Oxford, Clarendon Press

    Google Scholar 

  36. Ryan, M. (1992). Representing defaults as sentences with reduced priority. In B. Nebel, C. Rich, & W. Swartout (Eds.), Principles of knowledge representation and reasoning: Proceedings of the third international conference, KR ’92, Cambridge, MA, October 1992. (pp. 649–660). San Mateo: Morgan: Kaufmann.

  37. Sakama, C., & Inoue, K. (1996). Representing priorities in logic programs. In: M. Maher (Ed.), Joint international conference and symposium on logic programming JICSLP 1996, Bonn, September 1996 (pp. 82–96). Cambridge: MIT Press.

    Google Scholar 

  38. Sosa E. (1996). The logic of imperatives. Theoria 32, 224–235

    Article  Google Scholar 

  39. Świrydowicz K. (1994). Normative consequence relation and consequence operations on the language of dyadic deontic logic. Theoria 60, 27–47

    Article  MathSciNet  MATH  Google Scholar 

  40. von Wright G.H. (1968). An essay in deontic logic and the general theory of action. Amsterdam, North Holland

    Google Scholar 

  41. von Wright, G. H. (1984). Bedingungsnormen, ein Prüfstein für die Normenlogik. In W. Krawietz, H. Schelsky, O. Weinberger, & G. Winkler (Eds.), Theorie der Normen (pp. 447–456). Berlin: Duncker & Humblot.

  42. Watts, I. (1725). Logick: or, the right use of reason in the inquiry after truth, with a variety of rules to guard against error in the affairs of religion and human life, as well as in the sciences. London: for John Clark, Richard Hett et al.

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Correspondence to Jörg Hansen.

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Hansen, J. Prioritized conditional imperatives: problems and a new proposal. Auton Agent Multi-Agent Syst 17, 11–35 (2008). https://doi.org/10.1007/s10458-007-9016-7

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